Linear Programming exercise
ABC Ltd is a small factory which makes two components, C1 and C2. It has the following constraints on weekly production:
Operative time 240 staff hours
Raw material A 500 kg
Raw material B 400 litres
C1 uses two staff hours, 5 kg of A and 5 litres of B to make each unit.
C2 uses three staff hours, 5 kg of A and 4 litres of B to make each unit.
The contributions to profit from each unit of C1 and C2 are $150 and $100, respectively. It is known that all production can be sold.
Requirements
1. Represent the above situation as a linear programming model, if the object is to maximise total weekly profit. (Demote the units of C1 and C2 produced each week by X1 and X2 respectively.) (5 marks)
2. Show the constraints from (1) above on a graph and indicate the feasible region.
(7 marks)
3. Determine the product mix which will maximise weekly profit, and the maximum weekly profit, in (1) above. (7 marks)
4. State two limitations of linear programming. (6 marks)
(Total 25 marks)
Operative time 240 staff hours
Raw material A 500 kg
Raw material B 400 litres
C1 uses two staff hours, 5 kg of A and 5 litres of B to make each unit.
C2 uses three staff hours, 5 kg of A and 4 litres of B to make each unit.
The contributions to profit from each unit of C1 and C2 are $150 and $100, respectively. It is known that all production can be sold.
Requirements
1. Represent the above situation as a linear programming model, if the object is to maximise total weekly profit. (Demote the units of C1 and C2 produced each week by X1 and X2 respectively.) (5 marks)
2. Show the constraints from (1) above on a graph and indicate the feasible region.
(7 marks)
3. Determine the product mix which will maximise weekly profit, and the maximum weekly profit, in (1) above. (7 marks)
4. State two limitations of linear programming. (6 marks)
(Total 25 marks)
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